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Chapter 1: Problem 60

Sketch the straight line defined by the linear equation by finding the \(x\) - and \(y\) -intercepts. $$ 2 x+3 y-15=0 $$

Short Answer

Expert verified
\(x\)-intercept: \(x = 7.5\) #tag_title#Step 2: Find the \(y\)-intercept#tag_content# To find the \(y\)-intercept, let \(x = 0\) and solve for \(y\): $$ 2 (0) + 3y - 15 = 0 $$ \(y\)-intercept: \(y = 5\) #tag_title#Step 3: Plot the line#tag_content# Now, we can plot the line using the \(x\)-intercept (7.5, 0) and the \(y\)-intercept (0, 5) on a graph. Connect the points to form the straight line.

Step by step solution

01

Find the \(x\)-intercept

To find the \(x\)-intercept, let \(y = 0\) and solve for \(x\): $$ 2 x+3 (0) - 15=0 $$

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Most popular questions from this chapter

Use the results of Exercise 63 to find an equation of a line with the \(x\) - and \(y\) -intercepts. $$ x \text { -intercept }-2 ; y \text { -intercept }-4 $$

The following table gives the projected operations management consulting spending (in billions of dollars) from 2005 through \(2010(x=5\) corresponds to 2005 ): $$ \begin{array}{lcccccc} \text { Year, } \boldsymbol{x} & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline \text { Spending, } \boldsymbol{y} & 40 & 43.2 & 47.4 & 50.5 & 53.7 & 56.8 \\ \hline \end{array} $$ a. Find an equation of the least-squares line for these data. b. Use the results of part (a) to estimate the average rate of change of operations management consulting spending from 2005 through 2010 . c. Use the results of part (a) to estimate the amount of spending on operations management consulting in 2011, assuming that the trend continues.

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. Suppose the slope of a line \(L\) is \(-\frac{1}{2}\) and \(P\) is a given point on \(L\). If \(Q\) is the point on \(L\) lying 4 units to the left of \(P\), then \(Q\) is situated 2 units above \(P\).

Use the results of Exercise 63 to find an equation of a line with the \(x\) - and \(y\) -intercepts. $$ x \text { -intercept } 4 ; y \text { -intercept }-\frac{1}{2} $$

Determine whether the points lie on a straight line. $$ A(-2,1), B(1,7), \text { and } C(4,13) $$
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